An investment of $ was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was The interest from the first investment was times the interest from the second. Find the amounts of the three parts of the investment. What is the amount of the first part of the investment? $ nothing What is the amount of the second part of the investment? $ nothing What is the amount of the third part of the investment? $ nothing Enter your answer in each of the answer boxes.

18,000 is invested at 8%.

12,000 is invested at 6%.

20,000 is invested at 9%.

Explanation:

x = amount invested at 8%.

y = amount invested at 6%.

z = amount invested at 9%.

x + y + z = 50,000

.08x + .06y + .09z = 3960

interest on the first investment is equal to 2 times interest on the second investment.

.08x = 2 * .06y

solve for x to get x = .12y/.08 = 1.5y

since .08x = .12y, you can replace .08x with .12y.

since x = 1.5y, you can replace x with 1.5y

your two equations of x + y + z = 50,000 and .08x + .06y + .09z = 3960 become:

1.5y + y + z = 50,000

.12y + .06y + .09z = 3960

combine like terms in both equations to get: 2.5y + z = 50,000

.18y + .09z = 3960

you now have 2 equations with 2 unknown variables which can be solved simultaneously for a unique solution.

we will eliminate the z variable from the 2 equations in the following manner.

multiply both sides of the first eqution by 9 and multiply both sides of the second equation by 100.

you will get:

2.5y + z = 50,000 becomes 22.5y + 9z = 450,000.

.18y + .09z = 3960 becomes 18y + 9z = 396,000.

the 2 equations are now:

22.5y + 9z = 450,000

18y + 9z = 396,000

subtract the second equation from the first to get:

4.5y = 54,000

divide both sides of this equation by 4.5 to get:

y = 12,000

since x = 1.5y, then x must be equal to 18,000

since x + y + z = 50,000, then z must be equal to 20,000

you have:

x = 18,000

y = 12,000

z = 20,000

the interest on each of these investments is:

.08 * 18,000 = 1,440

.06 * 12,000 = 720

.09 * 20,000 = 1,800

add up the investments and you get 50,000

add up the interest and you get 3,960

the interest on the first investment is 2 times the interest on the second investment because 1,440 = 2 * 720.

all results are confirmed as good.

your solution is:

18,000 is invested at 8%.

12,000 is invested at 6%.

20,000 is invested at 9%.

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%